About simultaneity

Einstein in his "Relativity: The Special and General Theory" ch.VIII explains that simultaneity between events placed in two predetermined places A and B can be asserted if an observer in the mid-point M sees the light coming from the two events places in the same time.
In ch.VII he says that since "light speed is a constant in any Galilean Co-ordinate System" is an axiom, you can't add or subtract the observer velocity to the light speed: any observer, despite his Galilean Co-ordinate System of reference, must see light speed = c.
In ch.IX he explains the train experiment, and this looks inconsistent with the previous chapters: ina K Galilean Co-ordinate System of reference, events placed in A and B are simultaneous from the M mid-point of view, and when Einstein tells that the observer in M' mid-point on the carriage (K' GCS) sees the light coming from B earlier than the A he skates over any explanations. And the only explanation I can find is that he thinks the observer travelling at velocity w can be reached from the light coming from B earlier because in the mean time M' has moved forward from M to a place closer to B than M: this is equivalent to adding w and c and this is inconsistent with ch.VII assertion.
I think that if M' is the mid-point between A' and B' (places in K' corresponding to A and B in K when the events happen) he must see the A' and B' lights coming in the same time since he is in the mid-point and c is constant, and we can't take in account he is moving because that movement is just a K-K' relation and this relation can't affect independent measurements on K'. If I don't express the M' mid-point concept using A'-B' reference, I must argue that M' is not a mid-point anymore (it has moved and isn't in the middle of A-B segment anymore when the lights comes) and the definition of simultaneity is not applicable to M' so the experiment must result in a nonsense.
What do you think?

Staff: Mentor

Einstein in his "Relativity: The Special and General Theory" ch.VIII explains that simultaneity between events placed in two predetermined places A and B can be asserted if an observer in the mid-point M sees the light coming from the two events places in the same time.

Right. The observer at the midpoint between A and B can conclude that the events are simultaneous according to him.

In ch.VII he says that since "light speed is a constant in any Galilean Co-ordinate System" is an axiom, you can't add or subtract the observer velocity to the light speed: any observer, despite his Galilean Co-ordinate System of reference, must see light speed = c.

Right. The key here is that any observer will measure light to move at speed c with respect to himself.

In ch.IX he explains the train experiment, and this looks inconsistent with the previous chapters: ina K Galilean Co-ordinate System of reference, events placed in A and B are simultaneous from the M mid-point of view, and when Einstein tells that the observer in M' mid-point on the carriage (K' GCS) sees the light coming from B earlier than the A he skates over any explanations. And the only explanation I can find is that he thinks the observer travelling at velocity w can be reached from the light coming from B earlier because in the mean time M' has moved forward from M to a place closer to B than M: this is equivalent to adding w and c and this is inconsistent with ch.VII assertion.

No inconsistency here. The embankment observers measure the light from B as moving at speed c with respect to the embankment. There's no problem in having the embankment observers see M' move at speed w to the right and the light move at speed c to the left. The closing speed of M' and the light will be 'w+c' according to the embankment observers. Of course, according to the train observers the light travels at speed c with respect to the train. (Note that both the train observers and the embankment observers both see the light travel at speed c with respect to themselves.)

I think that if M' is the mid-point between A' and B' (places in K' corresponding to A and B in K when the events happen) he must see the A' and B' lights coming in the same time since he is in the mid-point and c is constant, and we can't take in account he is moving because that movement is just a K-K' relation and this relation can't affect independent measurements on K'. If I don't express the M' mid-point concept using A'-B' reference, I must argue that M' is not a mid-point anymore (it has moved and isn't in the middle of A-B segment anymore when the lights comes) and the definition of simultaneity is not applicable to M' so the experiment must result in a nonsense.

M' is definitely at the midpoint between A' and B'. But M' will only conclude that the events at A' and B' occurred simultaneously if the light from each reached M' at the same time. But we have shown, by viewing things from the embankment frame, that the light does not reach M' at that same time.

Relativity resolves the apparent paradox as follows: what is simultaneous for one observer might not be simultaneous for another observer in relative motion.

Try this. Suppose the observer, M, in the middle of the train aimed lasers at two clocks, one at the front of the train (A) and one at the rear of the train (B), at the very instant he passes the platform observer, M’. These are clocks M has previously synchronised. Suppose that the clocks stop when the laser hits them. If he inspects them later on, he’ll find that both clocks have stopped at the same time (say at 3 o’clock). There’s no surprise for him because a) he’s in the middle of the train and b) the light has travelled at the same speed towards each clock. (And if the train has no windows, is on a perfectly smooth track and makes no noise, he’d have no idea he was moving. He could, rightly, consider his train to be at rest from the point of view of relativity.)

Now the observer on the platform, M’, also observes the light moving at speed c in his own frame: this is regardless of direction and, most importantly, the source’s relative velocity to him. Just because the source is on a train moving past him, he’d still observe the light to move away from him towards the front of the moving train at speed c; and, equally, he’d observe the light to be moving away from him in the other direction, towards the back of the train, at speed c. The start point for the light in his frame is where he’s standing.

However, he would notice that the light aimed at the clock at the front of the train took longer to reach it than it took to reach the clock at the rear: M’ would observe that the forward-aimed light has to travel further because it is having to chase after the receding front clock; but M’ would also observe that the rear-aimed light has less distance to travel because the rear clock is moving towards the light. So he’d observe the rear clock to be stopped before the front clock. The stopping of the clocks is NOT simultaneous in his frame.

The conclusion he has to draw is that while the train’s clocks (and time) might be synchronised with each other in the frame of the train, they are not synchronised when observed from the platform frame. Simultaneity is relative and there is no paradox.

Maybe I've found my mistake: I've wrote that M' has moved and it isn't the mid-point anymore thence the simultaneity definition isn't applicable anymore to it. This is untrue, in fact the definition says that the observer must be in the mid-point when the events happen but it doesn't tell he can't move from there after the events happening and before the lights come to him.

Hi there. I have a little problem understanding this. If for the observer on the platform, the front of the carriage runs away from the light (as it actually does), so it does for the observer inside the train, right?

Staff: Mentor

Hi there. I have a little problem understanding this. If for the observer on the platform, the front of the carriage runs away from the light (as it actually does), so it does for the observer inside the train, right?

How does the light know? This isn't about some vagaries of perception, is it?

I wouldn't worry - it's not at all obvious. We're first educated in Newtonian mechanics etc. And, to many, that is amenable to an intuitive grasp - a bullet leaving the barrel of a moving gun has a different speed to one fired from a stationary gun, with the difference being the speed of the gun etc.

But relativity has as a basic principle/postulate/axiom (call it what you like) that the speed of light is always measured to have the same value, no matter how the source or the experimenter move relative to each other. This really was a shocker.

But innumerable experiments back it up. So people quickly got used to it and now we just accept it as 'that's what nature does'.

The upshot is that, if the Principle of Relativity is true, time and space can't be the inflexible things they were once thought to be - they just can't. Your everyday experience can't prepare you for this.

I'm so used to relativity that I might con myself into believing I've got some sort of intuitive grasp, but it's probably nothing more than mere familiarity.

But relativity has as a basic principle/postulate/axiom (call it what you like) that the speed of light is always measured to have the same value, no matter how the source or the experimenter move relative to each other. This really was a shocker.

That's not Einstein's second postulate. He didn't say that the speed of light is measured to be equal to c, he said the propagation of light is defined to be c. So when you have two clocks and you measure how long it takes a flash of light to go from the one to the other, and you divide the distance between them by the measured time difference between the two clocks and you calculate the speed of light to be something other than c, you tweak one of your clocks and repeat until the calculation comes out to be c. You're not measuring the propagation of light, you're defining it.

That's not Einstein's second postulate. He didn't say that the speed of light is measured to be equal to c, he said the propagation of light is defined to be c. So when you have two clocks and you measure how long it takes a flash of light to go from the one to the other, and you divide the distance between them by the measured time difference between the two clocks and you calculate the speed of light to be something other than c, you tweak one of your clocks and repeat until the calculation comes out to be c. You're not measuring the propagation of light, you're defining it.

I’m not sure that’s what he said.

In his 1905 paper, On the Electrodynamics of Moving Bodies, he said “We…also introduce another postulate, …, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body”, which he referred to as “the principle of constancy of the speed of light”

He didn’t say that you need to adjust your clocks and/or measuring rules so that they yield the velocity of light to be a certain value. I think it's definitely the other way round: if you have taken care to set up your measurement system unambiguously, especially with respect to synchronsiation, then you will find the speed of light to be c because it is invariant.

He carefully set up how you would measure position, time and how you would define synchronisation. The definition involving the speed of light referred only to the time for light to travel from one place to another being the same as it would take to make the return journey - this in order to establish a definition of synchronisation.

Staff: Mentor

In his 1905 paper, On the Electrodynamics of Moving Bodies, he said “We…also introduce another postulate, …, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body”, which he referred to as “the principle of constancy of the speed of light”

Yes, Einstein said is not is defined, but for present purposes it comes down to the same thing. If the postulate is that "light is always propagated in empty space with a definite velocity c..." and you measure anything else you conclude that your method of measuring is wrong.

That's not Einstein's second postulate. He didn't say that the speed of light is measured to be equal to c, he said the propagation of light is defined to be c. So when you have two clocks and you measure how long it takes a flash of light to go from the one to the other, and you divide the distance between them by the measured time difference between the two clocks and you calculate the speed of light to be something other than c, you tweak one of your clocks and repeat until the calculation comes out to be c. You're not measuring the propagation of light, you're defining it.

I’m not sure that’s what he said.

In his 1905 paper, On the Electrodynamics of Moving Bodies, he said “We…also introduce another postulate, …, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body”, which he referred to as “the principle of constancy of the speed of light”

He didn’t say that you need to adjust your clocks and/or measuring rules so that they yield the velocity of light to be a certain value. I think it's definitely the other way round: if you have taken care to set up your measurement system unambiguously, especially with respect to synchronsiation, then you will find the speed of light to be c because it is invariant.

He carefully set up how you would measure position, time and how you would define synchronisation. The definition involving the speed of light referred only to the time for light to travel from one place to another being the same as it would take to make the return journey - this in order to establish a definition of synchronisation.

Einstein's synchronization process is implementing his definition of the propagation of light. Look at these words:

In accordance with definition the two clocks synchronize if tB-tA=t'A-tB.

Now what are you supposed to do if the clocks do not synchronize according to his definition? Obviously, you tweak one of them until they do. And once you do this, then when you do it again, you will "measure" the one-way speed of light to be c. Do you really think you are making a measurement or merely confirming your previous adjustment of your clocks?

Plus, look at how many times Einstein uses the words "defined" or "definition", including in the title of section 1 of his paper.

I think that you are not exactly right. As I see the key words are "which is independent of the state of motion of the emitting body". Basically for particular observer all light moves at the same speed irrespective of source.

And you don't need to postulate a definition, you just give it i.e. in definition you don't assume that things work in particular way you just say how you will name something.

Einstein's synchronization process is implementing his definition of the propagation of light. Look at these words:

In accordance with definition the two clocks synchronize if tB-tA=t'A-tB.

Now what are you supposed to do if the clocks do not synchronize according to his definition? Obviously, you tweak one of them until they do. And once you do this, then when you do it again, you will "measure" the one-way speed of light to be c. Do you really think you are making a measurement or merely confirming your previous adjustment of your clocks?

Einstein's synchronization process ensures that speed of light is the same in opposite directions and that takes away major part of mystery. But this synchronization procedure can not make speed of light isotropic (the same in any direction not just opposite directions).

As I see the key words are "which is independent of the state of motion of the emitting body". Basically for particular observer all light moves at the same speed irrespective of source.

Einstein's synchronization process ensures that speed of light is the same in opposite directions and that takes away major part of mystery. But this synchronization procedure can not make speed of light isotropic (the same in any direction not just opposite directions).

Of course the synchronization procedure makes the measured speed isotropic.

It is the same procedure in any direction how could it not work in every direction???

I think that you are not exactly right. As I see the key words are "which is independent of the state of motion of the emitting body". Basically for particular observer all light moves at the same speed irrespective of source.

This is one aspect of the one-way speed of light that we can measure, that is, light that is coming from two sources with a relative speed between them in line with the observer can be measured to travel at the same speed, but we cannot measure what that speed is. Einstein is defining that speed to be c.

Einstein's synchronization process ensures that speed of light is the same in opposite directions and that takes away major part of mystery. But this synchronization procedure can not make speed of light isotropic (the same in any direction not just opposite directions).

Not according to Einstein. Look at his words in section 1:

We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid:—

And he then proceeds to state that although clock A and clock B must of course be in line, clock C can be anywhere, not just in line with A and B.